After 10 days of WODB warmups we went back to Estimation 180 with malted eggs in a cylinder. It was Day 122 (http://www.estimation180.com/day-122.html). I made sure I had a student report out on estimating 1 layer of 9 eggs, and thinking it was 9 layers tall. I related this to the general formula for volume of 3D solids. Volume equals the area of the base times the height.
After grading last week's assessments I was concerned about students understanding of exponents and transversals cutting parallel lines.
|This was one of the few students who aced the last exponent question and showed their work very clearly.|
|Unfortunately students confusion with integers kept them from demonstrating their understanding of exponent laws.|
Then I had students turn a piece of binder paper with the 3 holes up in landscape mode. I then had them trace a ruler twice. I asked them what types of lines these made (parallel). I then asked them what do we call the line that intersects a pair of lines? (transversal). Then I labeled angles A and B and asked if the angles were the same or if they added to 180 degrees. They said the same. I asked them if they were congruent or supplementary. Congruent. Great, got the vocabulary established. Then I asked them why they were congruent and asked for a raise of hands. Students said they were corresponding angles. I added that it's also because the transversal cuts parallel lines.
I then moved on to labeling C and D. There were mixed responses if they were the same or added to 180. Because they could be traced with tracing paper and rotated to be matched up, they were the same or congruent. I asked students if the were in between or outside the parallel lines. In between, oh so on the interior. Were the angles on the SAME SIDE of the transversal or on different sides? Different. Oh, so those are alternate sides. Put it together and you have alternate interior angles.
Then I added angle E across from B. They said it was the same and only a few students remembered why. They are vertical angles and therefore congruent. Then on the lower lines I made F and G and they said they were supplementary. I then used the same line of questioning. Interior or exterior of parallel lines? Interior. Same side or alternate sides? Same side. So, same side interior.
Then I added angle H, and they said it was supplementary. The two angles formed a straight angle. I then asked what you call 2 angles that are next to each other. Only about 1 student in each class remembered the word from 7th grade: adjacent. In a few classes I mentioned we all have next door neighbors. Mathematically, they'd be called our "adjacent neighbors."
Then students practiced in lesson 9.1.1 on identifying the relationship between pairs of angles. They finally saw another example of a pair of lines that were not parallel being intersected by a transversal. They clearly saw they weren't parallel, but did not make the connection that they could still be called corresponding angles, they just wouldn't have the property of being congruent. So, the day of reteaching had commenced.
Then in accelerated I passed out a worksheet from Math Equals love about memorizing the quadratic formula by reciting it to 3 different people. They then worked on the first section of chapter 10 about two way frequency tables. We didn't get to discussing that part because students presented their methods of filling out the venn diagram. Interesting, students tallied all the survey results, 182, and subtracted 175, the number of students surveyed to get 7. They reported that this difference were the number of voters whose votes were tallied twice and therefore had both a piPhone and a laptop. Then they subtracted 7 from the phone results and 7 from the 44 results.
They didn't understand how there could be a different way. I saw it completely different and took the 175 students surveyed and subtracted the students who had neither a phone or a laptop to get 65. That means 65 had one or the other. I then subtracted the 28 votes for piPhone from 65 and got 37. There were 37 students who had only a laptop. 65 minus the 44 who had laptops gave me 21 who had only a phone. Students thought my way was very time consuming, and I suppose it was.
Below is a dot talk from Steve Wyborney that I want to print out on quarter sheets of paper and use as a warmup and suggest my colleagues do as well. So students would have a chance to mark up the circles and write their own expressions and those that their peers come up with.